Work is classically calculated as force x displacement, i.e., F x d, gm.cm^2/sec^2 x cm.However, when you hold an object up and prevent it from falling, energy is being expended even though no distance is traversed. I have gone back to my college physics book (Sears and Zymansky) but they don't say anything about it. How do you calculate the energy expenditure (in cal or Kcal, say) when no motion occurs?

All the energy spent in this case is at a cellular level.The energy being spent is going toward keeping your arm steady - and will eventually be dissipated as heat.As far as how to measure or calculate this - I have no idea.